3x - 4y = 16
5x = 6y = 14

can you please correct your question - how could the second equation have two equal signs?

I added an extra = by mistake its

3x - 4y = 16
5x + 6y = 14

Multiply by 3 both sides in the first equation, multiply by 2 both sides in the second equation, then sum side by side the 2 equations.

Alternatively, multiply by 5 both sides in the first equation, multiply by 3 both sides in the second equation, then subtract side by side the 2 equations.

Try to eliminate one variable by multiplying both equations and the subtracting them form each other. This will likely get you one of the variable values. Once that's done, you simply substitute into one of the equations and solving for the remaining variable. So, let's try this

Let's say you've got these equations:
(1) 10x - 12y = 24
(2) 7x + 4y = 48

My first thought is to find the value of y so I'll try to eliminate x. I'll multiply by 7 for Eq.(1) and 10 for Eq.(2) giving me:
(1') 70x - 84y = 168
(2') 70x + 40y = 480

Now I subtract the two giving me:
-124y = -312
I can solve for y
y = 312/124 (or 2.51612)

Substituting this in for the above equation (1), I can solve for x now:
(3) 10x - 12*(312/124) = 24

(4) 10x = 24 + 12*(312/124)

x = 5.41935

You should, of course, double check your work. I'll use Eq. (1):
10*(5.41935) - 12*2.51612 ~= 24 (rounding error)

The trick is to find the right numbers to multiply your equations with so they cancel each other out. As you probably noticed, I'm using multiples that will give the same number of x's (or y's) in both equations allowing me to subtract that variable out.

Good luck.